AMUEEE Set 2AMUEEE Set 2

Duration : 3 : 00 HrsDuration : 3 : 00 Hrs

Exam

AMUEEETotal Questions

150Marks for Correct Answer

1Negative Marks

0.25Physics

50Chemistry

50Mathematics

50

PhysicsPhysics

1. The velocity of a transverse wave in a string is directly proportional to and inversely proportional to . In a measurement, themass applied at the end of string is 3.0 g, length of string is 1 m and mass of string is 5 g. If possible error in measuring mass is 0.1 g andthat of length is 1mm, the percentage error in measurement of velocity is (a) 4.5% (b) 2.7% (c) 2.1% (d) 3.7% Correct: b 2. If reaction is R and coef�cient of friction , what is the work done against friction in moving a body by distance d?

(a) (b) (c)

(d)

Correct: c 3. Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangentialvelocities are v and 2v respectively, as shown in the �gure. Between collisions, the particles move with constant speeds. After makinghow many elastic collisions, other than that at A, these two particles will again reach the point A?

(a) 4 (b) 3 (c) 2 (d) 1 Correct: c 4. The displacement of a body is given by where x is in metre and t is in second. The difference between the averagevelocity of the body in the time-interval t =1 s to t= 2 s and its instantaneous- velocity at t=1s is (a) 20.0 m/s (b) 22.5 m/s (c) 27.0 m/s (d) 39.0 m/s Correct: a

√T √u

μr

μrRd

4

2μr,RdμrRdμtRd

2

x = 4t + 5t3

Admission aglasem

5. A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward followed again by 5 steps forward and 3 stepsbackward and so on. Each step is 1m long and requires 1s. Determine how long the drunkard takes to fall in a pit 13 m away from thestarting point? (a) 37 s (b) 13 s (c) 49 (d) 18 s Correct: a 6. A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d/2. Neglectingsubsequent motion and air resistance, its velocity v varies with the height h above the ground as

(a)

(b)

(c)

(d) Correct: b 7. Two seconds after projection, a projectile is moving at 30° above the horizontal, after one more second, it is moving horizontally. The initial speed of the projectile is (Take ) (a) 10 m/s (b) 10/3 m/s (c) 20 m/s (d) 2013 m/s Correct: d 8. A thin circular ring of mass M and radius r is rotating about its axis at angular velocity . Two particles, each of mass m are attachedgently to the ring at points which are at opposite ends of diameter of the ring. New angular velocity of the ring is (a)

(b)

(c) (d)

Correct: a 9. A particle of mass m is moving with a constant velocity along a line parallel to the positive direction of X-axis. The magnitude of itsangular momentum with respect to the origin (a) is zero. (b) goes on increasing as x increases. (c) goes on decreasing as x increases. (d) remains constant for all positions of the particle. Correct: d 10. A satellite of mass M is revolving in circular orbit of radius r around the earth. Time of revolution of the satellite is

g = 10ms−2

ω

Mω

M+2mω(M+2m)

M

ωωm

(M+2m)

Admission aglasem

(a)

(b)

(c)

(d) Correct: b 11. One end of massless spring of spring constant 100 N/m and natural length 0.49 m is �xed and other end is connected to a body ofmass 0.5 kg lying on a frictionless horizontal table. The spring remains horizontal. If the body is made to rotate at an angular velocity of2 rad/s, then the elongation of the spring will be (a) 2 cm (b) 1 cm (c) 0.5 cm (d) 0.25 cm Correct: b 12. A disc of mass M and radius R is rolling with angular speed on a horizontal surface as shown in �gure. The magnitude of angularmomentum of the disc about the origin O is (here v is the linear velocity of the disc)

(a) (b) (c) MRv (d)

Correct: d 13. The only force acting on a 2 kg body that is moving in xy-plane has a magnitude of 5 N. The body initially has a velocity of 4 m/s inthe positive x-direction. Some time later, the body has a velocity of 6 m/s in the positive y-direction. The work done on the body by the5 N force during this time is (a) 20 J (b) 40 J (c) 52 J (d) 72 J Correct: a 14. A simple pendulum has time period . The point of suspension is now moved upward according to the relation

where y is the vertical displacement. The time period now becomes .

The ratio of is

(a) 5/6 (b) 6/5 (c) 1 (d) ⅘ Correct: b 15. Figure shows a rectangular copper plate with is centre of mass at the origin O and side AB = 2BC = 2 m. If a quarter part of the plate(shown as shaded) is removed, the centre of mass of the remaining plate would lie at

(a)

(b)

(c)

(d)

T ∝ r12

T ∝ r3

2

T ∝ r−1

2

T ∝ r−3

2

ω

MR2ω232

MR2ω

MRv32

T1

y = kt2, (k = 1m/s2) T2

T 21

T 22

(g = 10m/s2)

m, m112

16

m, m16

112

m, m13

16

m, m13

12

Admission aglasem

Correct: b 16. Two long conductors, separated by a distance d carry currents in the same direction. They exert a force F on each other.Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to 3d. The newvalue of force between them is (a) - 2F (b) F/3 (c) -2F/3 (d) -F/3 Correct: c 17. Two identical cells are �rst connected in series and then in parallel. The ratio of power consumed by them is (a) 1:1 (b) 1:2 (c) 1:3 (d) 1:4 Correct: a 18. Three particles, two with masses m and one with mass M, might be arranged in any of the four con�gurations shown below. Rankthe con�gurations according to the magnitude of the gravitational force on M, least to greatest

(a) (i), (i), (iii), (iv) (b) (ii), (i), (iii), (iv) (c) (ii), (i), (iv), (iii) (d) (ii), (iii), (iv), (i) Correct: b 19. A cylinder of radius R made of a material of thermal conductivity , is surrounded by a cylindrical shell of inner radius R and outerradius 2R and made of a material of thermal conductivity . The two ends of the combined system are maintained at two differenttemperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivityof the system is (a)

(b)

(c) (d)

Correct: b 20. The strength of current i in the given �gure is

(a) 1.7 A (b) 1.3 A (c) 3.7 A (d) 1.0 A Correct: a 21. Two solid spheres of the same metal but of mass M and 8 M fall simultaneously in a viscous liquid. If their terminal velocities are vand nv, then the value of n will be (a) 16 (b) 8 (c) 4

I1 and I2

K1

K2

3K1+K2

4K1+3K2

4

K1 + K2K1K2

K1+K2

Admission aglasem

(d) 2 Correct: c 22. 1A current �ows through an in�nitely long straight wire. The magnetic �eld produced at a point 1 m away from it is (a) (b)

(c) (d) Correct: c 23. The rms value of potential difference shown in �gure is

(a) (b)

(c)

(d)

Correct: b 24. A sample of an ideal gas undergoes an isothermal process as shown by the curve AB in the pV diagram. If represent the amount of heat absorbed the change in internal energy and the work done respectively, then which of the followingstatement is correct?

(a) (b) (c) (d) Correct: b 25. An electric �eld exists in space. Then, the potential difference , where Vo is the potential at the origin and isthe potential at x=2 m, is given by (a) (b) (c) (d) Correct: a 26. A rocket is moving at a speed of 200 m/s towards a stationary target. While moving it emits a wave of frequency 1000 Hz. Some ofthe sound reaching the target gets re�ected back to the rocket as an echo. The frequency of the echo as detected by the rocket is(velocity of sound = 330 m/s) (a) 1000 Hz (b) 1580 Hz (c) 2540 Hz (d) 4080 Hz Correct: d 27. A copper ring having a cut such that it does not form a complete loop is held horizontally and a bar magnet is dropped through thering with its length along the axis of the ring. Then acceleration of the falling magnet is

2 × 10−3TT2

10

2 × 10−7T2π × 10−6T

V0

V0V0

√2V0

2V0

√3

ΔQ, ΔU  and ΔW

ΔQ = + ve, ΔU = 0, ΔW = −ve

ΔQ = +vθ, ΔU = 0, ΔW = +ve

ΔQ = +vθ, ΔU = 0, ΔW = 0ΔQ = +ve, ΔU = +ve, ΔW = +ve

→E = 30x2 i VA − Vo VA

−80j

120j

−120j

80j

Admission aglasem

(a) g (b) less than g (c) more than g (d) zero Correct: a 28. Figure shows three arrangements of electric �eld lines. In each arrangement, a proton is released from rest at point A and then iaccelerated through point B by the electric �eld. Points A and B have equal separations in the three arrangements. If arelinear momentum of the proton at point B in the three arrangement respectively, then

(a) (b) (c) (d) Correct: b 29. The electromagnetic wave used in LASIK eye surgery is (a) ultraviolet ray (b) X-ray (c) microwave (d) radio wave Correct: a 30. Two bulbs consume the same power when operated at 200 V and 300 V, respectively. When these bulbs are connected in seriesacross a DC source of 500 V, then the ratio of potential difference across them is (a) 2/3 (b) 4/9 (c) 6/27 (d) 8/24 Correct: b 31. Two identical conducting spheres A and B carry equal charge. They are initially separated by a distance much larger than theirdiameters and the force between them is F. A third identical conducting sphere C is uncharged. Sphere C is �rst touched to A, then to Cand removed. As a result, the force between A and B now is (a) F/16 (b) F/4 (c) 3F/8 (d) F/2 Correct: c 32. The bending of beam of light around corners of obstacles is called (a) re�ection (b) refraction (c) diffraction (d) interference Correct: c 33. An inverter battery operated on 24 V and has negligible internal resistance. It is rated at 140 ampere-hour. What external resistancewould have to be connected to the battery, if it were to be discharged in 14 hours. (a)

p1, p2 and p3

p1 > p3 > p2

p1 > p2 > p3

p2 > p1 > p3

p1 = p2 = p3

1.6Ω

Admission aglasem

(b) (c) (d) - Correct: b 34. Light travels in a straight line because (a) it is not absorbed by atmosphere (b) its velocity is very high (c) diffraction effect is negligible (d) None of the above Correct: c 35. Mirage is a phenomenon due to (a) re�ection of light (b) refraction of light (c) total internal re�ection of light (d) diffraction of light Correct: c 36. Two long straight wires vertically pierced the plane of the paper at vertices of an equilateral triangle as shown in �gure. They eachcarry 2 A, out of the paper. The magnetic �eld at the third vertex P has magnitude.

(a) (b) (c) (d) Correct: c 37. There are four lenses of focal lengths, 2, 4, 6 and 8 cm respectively. Two of these lenses form a telescope oflength 10 cm and magnifying power 4. The objective and eye lenses are (a) (b) (c) (d) Correct: d 38. A magnetic �eld cannot (a) change the velocity of a charged particle. (b) change the momentum of a charged particle. (c) change the kinetic energy of a charged particle. (d) change the trajectory of a charged particle. Correct: c 39. The de-Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 m/s is Given: Planck's constant =6.63x 10 34 J s (a) (b) (c) (d) Correct: d 40. What will be the ratio of de-Broglie wavelengths of proton and a-particle of the same energy? (a) 2:1 (b) 1:2 (c) 4:1

2.4Ω5.9Ω10.0Ω

10−5T

14 × 10−5T17 × 10−5T0.85 × 10−5T

L1,L2,L3 and L4

L2,L3

L1,L4

L3,L2

L4,L1

10−16m10−25m10−31m10−33m

Admission aglasem

(d) 1:4 Correct: a 41. An alternating voltage volt is connected to a capacitor through an AC ammeter. The reading of the ammeter (a) 40 mA (b) (c) 20 mA (d) Correct: c 42. In Young's double slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen wherethe path difference is λ, is k units. The intensity of the light at a point, where path difference is λ/3 is (a) k/2 (b) k/3 (c) k/4 (d) 2k/3 Correct: c 43. The mass-defect in a nuclear fusion reaction is 0.3 per cent. The amount of energy released in one kg of fusion reaction is (a) (b) (c) (d) Correct: d 44. In a stack of three polarising sheets, the �rst and the third are crossed while the middle one has its axis at 45° to the axes of theother two. The fraction of intensity of an incident unpolarised beam of light that is transmitted by the stack is (a) ½ (b) ⅓ (c) ¼ (d) ⅛ Correct: d 45. A proton (p) and an -particle are accelerated through the same potential difference V volt. The de-Broglie wavelengths associatedwith the proton and the respectively are in the ratio (a) 2:1 (b) (c) 4:1 (d) Correct: b 46. The wave nature of electron was �rst experimentally veri�ed by (a) Louis Victor de-Broglie (b) James Frank and Gustav Hertz (c) C.J. Davisson and L.H. Germer (d) Hans Geiger and Ernst Marsden Correct: a 47. In a semiconductor crystal if the current �ows due to breakage of crystal bonds, then the semiconductor is called (a) donor (b) acceptor (c) intrinsic semiconductor (d) extrinsic semiconductor Correct: c 48. In adjoining �gure, the input (A.C.) is across the terminals A and C and the output is across B and D. Then output is

V = 200√2 sin(100n) 1μF

20√2mA

10√2mA

2.7 × 1023J2.7 × 1019J2.7 × 1016J2.7 × 1014J

α

α -particle, λp and λα

2√2 : 1

√2 : 1

Admission aglasem

(a) zero (b) the same as input (c) half wave recti�ed (d) full wave recti�ed Correct: d 49. Consider the following (i) Submarine communications (ii) A.M. radio (iii) Shortwave ratio (iv) Radar Arrange the above in increasing frequency of the waves associated with them (a) (iv), (iii), (ii), (i) (b) (i), (ii), (iii), (iv) (c) (ii), (i), (iv), (iii) (d) (ii), (iii), (iv), (i) Correct: b 50. For a CE transistor ampli�er the audio signal voltage across the collector resistance of is 2 V. The current ampli�cation factorof the transistor is 100. If the base resistance is , the input signal voltage and base current are respectively (a) 0.01 V, 10 μA (b) 0.04 V, 10 μA (c) 0.01 V, 10 μA (d) 0.04 V, 10 μA Correct: a

ChemistryChemistry

51. Aniline is insoluble in water and possesses a vapour pressure of 10.15 mm Hg at 373 K. It can be conveniently puri�ed by (a) sublimation (b) crystallisation (c) steam distillation (d) simple distillation Correct: c 52. Which of the following has the maximum vapour pressure? (a) HCI (b) HBr (c) Hf (d) HI Correct: a 53. IUPAC name of is (a) 3, 3, 3-trimethyl-1-propene (b) 1, 1, 1-trimethyl-2-propene (c) 3, 3-dimethylbut-1-ene (d) 2,2-dimethyl-3-butene Correct: c 54. Which of the following is most soluble in water? (a) (b) (c)

2kΩ1kΩ

(CH3)3C − CH = CH2

CsClO4

NaClO4

kClO4

Admission aglasem

(d) Correct: d 55. The reaction,

(a) Etard's reaction (b) Sandmeyer's reaction (c) Wurtz-Fittig reaction (d) Perkin's reaction Correct: b 56. What is the compound 'C' in the following sequence of the reaction,

(a) Benzoic acid (b) Salicylic acid (c) Benzaldehyde (d) Salicylaldehyde Correct: b 57. In the reaction sequence

the product 'C' is (a) 1-propanol (b) 2-butanol (c) 2-butanol (d) 2-pentanol Correct: d 58. Arrange the following carbanions in order of their decreasing stability (i) (ii) (iii) (a) i > ii > iii (b) ii > i > iii (c) iii > ii > i (d) iii > ii > i Correct: b 59. The following reaction, is known as (a) Swarts reaction (b) Finkelstein reaction (c) Sandmeyer's reaction (d) Wurtz-Fittig reaction Correct: b

LiClO4

H3C − C ≡ C−

H − C ≡ C−

H3C − CH−2

R − X + Nal → R − I +  NaX where, X = Cl, Br

Admission aglasem

60. The crystal �eld splitting energy (CFSE) for is about What would be the CFSE value of (a) (b) (c) (d) Correct: b 61. The fastest dehydration reaction could be expected in

(a) (b) (c)

(d) Correct: a 62. Amongst the following interhalogen compounds which one is used for the production of during enrichment process? (a) (b) (c) (d) Correct: a 63. Which one of the following is known as animal starch? (a) Amylose (b) Cellulose (c) Glycogen (d) Amylopectin Correct: c 64. Nucleotides are joined together by between 5' and 3’ carbon atoms of pentose sugar (a) glycosidic linkage (b) peptide linkage (c) ether linkage (d) phosphodiester linkage Correct: d 65. The drug which was designed to prevent the interaction of histamine with the receptors present in the stomach wall (a) cimetidine (b) nardil (c) iproniazid (d) phenelzine Correct: a 66. What is the IUPAC name for the following compound?

(a) 1,3 - pentamethyl propane

[CoCl6]4− 18000cm−1 [CoCl4]2−?

18000cm−1

8000cm−1

16000cm−1

2000cm−1

CH3 − CH2 − CH2 − OHCH3 − (CH2)4 − OH

UF6235U

ClF3

ClF5

IF3

IF5

Admission aglasem

(b) 1, 1, 3, 3-tetramethylbutane (c) 2, 4, 4-trimethylpentane (d) 2, 2, 4-trimethylpentane Correct: d 67. Which one of the following set of metals deposits an anode mud during the process of electrolytic re�ning of copper? (a) Sn and Ag (b) Pb and Zn (c) Ag and Au (d) Fe and Ni Correct: c 68. Which of the following has highest hydration energy? (a) (b) (c) (d) Correct: a 69. The structure of is (a) square planar (b) distorted tetrahedral (c) angular (d) T-shaped Correct: d 70. For complexes and which one of the following statement is true

(a) is diamagnetic while is paramagnetic and both the complexes have square planar geometry.

(b) is paramagnetic while is diamagnetic and both the complexes have tetrahedral geometry.

(c) is paramagnetic while is diamagnetic and both the complexes have square planar geometry.

(d) is diamagnetic while is paramagnetic and both the complexes have tetrahedral geometry Correct: b 71. Ziegler catalyst to manufacture polyethylene is made by the reaction (a) (b) (c) (d) Correct: a 72. Primary valency of Co in Cl is (a) + 1 (b) + 2 (c) + 3 (d) + 6 Correct: c 73. The most reactive to nucleophilic attack at the carbonyl group is

(a)

MgCl2CaCl2BaCl2SrCl2

BrF3

[NiCl4]2− Ni(CO)4

[NiCl4]2− [Ni(CO)4]

[NiCl4]2− [Ni(CO)4]

[NiCl4]2−

[Ni(CO)4]

[NiCl4]2− [Ni(CO)4]

TiCl4 with Al(CH3)3

TiCl4 with CH3ClTiCl4 with (C6H5)3CCl

TiCl4 with ZnCl2

[Co(en)2Cl2]

Admission aglasem

(b)

(c)

(d) Correct: b 74. By the action of conc. , phosphorus changes to (a) phosphorus acid (b) orthophosphoric acid (c) metaphosphoric acid (d) pyrophosphoric acid Correct: b 75. Tear gas is (a) (b) (c) (d) Correct: a 76. Which of the following statements is wrong about the oxides of nitrogen? (a) is an anhydride of (b) NO is in acidic oxide (c) is an anhydride of (d) No is not an anhydride of an acid Correct: c 77. Inert pair effect is concerned with (a) pair of s-electrons (b) pair of p-electrons (c) pair of d-electrons (d) pair of f-electrons Correct: a 78. Copper is extracted from sulphide ore using the method (a) auto-reduction (b) carbon reduction (c) CO reduction (d) biochemical reduction Correct: a 79. The photochemical smog is (a) formed due to oxidation of hydrocarbons trapped in �owing air in the presence of sunlight (b) formed due to oxidation of smoke trapped in stagnant air mass in the presence of sunlight (c) formed due to heterogeneous combination of smoke and fog in air in the presence of sunlight (d) formed due to oxidation of hydrocarbons trapped in stagnant air mass in the presence of sunlight. Correct: d

H2SO4

CCl3NO2

COCl2ClC2H4 − S − C2H4ClC6H5 ⟶ S − Br

N2O5 HNO3

N2O3 HNO2

Admission aglasem

80. A compound (A) forms a phenyl hydrazone and gives negative Tollen's test and a positive Iodoform reaction. It also givesn-pentane on reduction. The compound (A) is (a) pentanal (b) 2-pentanone (c) 3-pentanone (d) allyl alcohol Correct: b 81. Which of the following chelating ligands can be used to remove the excess of copper in the biosystems? (a) D-penicillamine (b) Desferrioxamine B (c) EDTA (d) Dimercaprol Correct: a 82. Which of the following is an example of thermosetting polymers? (a) Bakelite (b) PVC (c) Nylon 6, 6 (d) Buna-S Correct: a 83. Arrange H20, H2S and H Se in order of increasing acidity. (a) H20 (a) (b) (c) (d) Correct: a 86. The root means square velocity of hydrogen at STP is and its means free path is . What will bethe collision number at STP? (a) (b) (c) (d) Correct: a 87. Which of the following gases has high Boyle's temperature? (a) Ar (b) (c) (d) He Correct: b 88. The difference between and is [ and signify molar quantities] (a) larger in case of gases in comparison to solids and liquids (b) larger in case of liquids in comparison to gases and solids (c) larger in case of solids in comparison to gases liquids (d) equal in solids, liquids and gases Correct: a 89. The rate of chemisorption of a gas (a) decreases with increasing pressure (b) increases with increasing pressure (c) is independent of pressure (d) is independent of temperature

C5H10O

T1 < T2 < T3

T3 < T2 < T1

T2 < T3 < T1

T1 < T3 < T2

1.83 × 105cm sec−1 1.78 × 10−5cm

9.476 × 109 sec−1

9.746 × 10−9 sec−1

9.746 × 109 sec−1

9.647 × 109 sec−1

CO2

O2

¯¯C p

¯¯CV

¯¯C p

¯¯CV

Admission aglasem

Correct: b 90. The reaction quotient (Q) for the reduction of to in acid solution,

is, [where, = activity of = pressure of , when it is present in the reaction, = pressure of at standard state)].

(a)

(b)

(c)

(d)

Correct: a 91. Water + mixture shows positive deviation from ideal solution behaviour. 100mL of water is mixed with 100mL of .Then, total volume of the mixture will be (a) 200 mL (b) less than 200 ml because of additional H-bonding between (c) more than 200 ml because H-bonding within molecules vanishes. (d) more than 200 mL because H-bond between is weaker than that between and Correct: d 92. 0.02 molar solution of NaCl having degree of dissociation of 90% at 27° C has osmotic pressure equal to (a) 0.94 bar (b) 9.4 bar (c) 0.094 bar (d) 9.4 x bar Correct: a 93. The �rst order gaseous decomposition of into has a k value of at 1°C and an energy of activation of 58 kJ

. At what temperature would be ? (a) 274 K (b) 283 K (c) 273 K (d) 293 K Correct: c 94. For the reaction, , . Therefore, E for the reaction should be

(a) (b) (c) (d) Correct: a 95. The ratio of the half-life time to the three quarter life-time, , for a reaction that is second order (a) depends directly on concentration of reactants (b) is independent of concentration of reactant (c) depends inversely on the concentration of reactants (d) depends directly to the square of concentration of reactants Correct: b 96. For a second order reaction, (2A Product), vs t is represented as

(a)

O2 H2OO2(g) + 4H+(aq) + 4e−

⟶ 2H2O(l)

αH+ H+, pO2O2 p0 O2

Q =p∘

α4H++p02

Q =PO2

α4H++ρ∘

Q =α4H++ρ02

p∘

Q =α4H++p0

p02

CH3OH CH3OH

H2O and CH3OHH2OH2O and CH3OH H2O H2O

10−4

N2O4 NO2 4.5 × 103s−1

mole−1 1.00 × 104s−1?

S( rhombic ) + O2 → SO2 ΔH = −298kJmol−1 at 25∘C and 1atm

−298kJmol−1

−298 + 8.314 × 298kJmol−1

−298 − 8.314 × 298kJmol−1

−298 − 2 × 8.314 × 298kJmol−1

(t1/2) (t3/4)

1[A]

Admission aglasem

(b)

(c)

(d) Correct: a 97. The solubility of pure oxygen in water at 20°C and 1.0 atmosphere pressure is mol/litre. What will be the concentrationof oxygen at 20°C and partial pressure of 0.21 atmosphere? (a) mol/litre (b) mol/litre (c) mol/litre (d) mol/litre Correct: a 98. Calculation the maximum work done in expanding 16 g of oxygen at 300K and occupying a volume of isothermally untilvolume becomes 25 (a) (b) (c) (d) Correct: a 99. The of and , are and respectively at 298 K. The concentration of ions in asaturated reactants solution containing and is (a) (b) (c) (d) Correct: b 100. In a suspension the diameter of the dispersed particles is of the order (a) 10 Å (b) 100 Å (c) 1000 Å (d) 2000 Å Correct: d

MathematicsMathematics

101. The value of is (a) 0.96 (b) 0.80 (c) 0.64 (d) 0.18

138 × 10−3

2.9 × 10−4

5.8 × 10−4

7.6 × 10−4

11.6 × 10−4

5dm3

dm3

−2.01 × 103J+2.01 × 103J1.20 × 1022

2 × 10−3

Ksp PbCO3 PbCO3 1.5 × 10−15 1 × 10−15 Pb2+

MgCO3 PbCO3

1.5 × 10−8M3 × 10−8M2 × 10−8M2.5 × 10−8M

sin(2 sin−1 0.8)

Admission aglasem

Correct: a 102. Let P = { denotes the greatest integer function is (a) (b) Q ⊄ P (c) P ⊄ Q (d) P = Q Correct: d 103. The function f(x) = x -[x] where I ] denotes the greatest integer function is (a) continuous everywhere (b) continuous at integer points only (c) continuous at non-integer points only (d) nowhere continuous Correct: c 104. The value of the integral is

(a)

(b)

(c)

(d) Correct: b 105. The range of the function f(x) = , is

(a) R (b) R - { - 1} (c) R - { 1 } (d) R - { 2 } Correct: b 106. Let R and S be any two equivalence relations on a set X. Then which of the following is incorrect statement (a) R U S is an equivalence relation on X (b) is an equivalence relation prix (c) is an equivalence relation on X (d) is an equivalence relation on X, where is the diagonal relation on X. Correct: a 107. Using the information from the �gure, is equal to

(a)

(b)

(c)

(d)

Correct: c

108. Let f (x) be a function de�ned by exists

(a) -2 (b) -1 (c) 0 (d) 1

P = θ; sin θ − cos θ = √2 cos θ}

P ⊂ Q and Q − P = ϕ

∫0

−2dx

√12−x2−4xπ

2π

6π

3

− π6

2+x

2−xx ≠ 2

R−1

R−1 ∩ S−1

Δ Δ

cos−1 x

+ cosxπ

2

+ sinxπ

2

− sin−1 xπ

2

+ sin−1 xπ

2

f(x) = {4x − 5,  if x ≤ 2

x − λ,  if x > 2 if  limx→2 f(x)

Admission aglasem

Correct: b 109. The graph divides the plane into regions. Then, the area of bounded regions is (a) 500 sq units (b) 1250 sq units (c) 2500 sq units (d) 800 sq units Correct: b 110. The equation of the circle whose radius is 5 and which touches the circle

externally at the point (5,5) is (a) (b) (c) (d) None of the above Correct: a 111. The variance of 20 observations in 5. If each observation is multiplied by 2, then the variance of the resulting observation is (a) 10 (b) 20 (c) 30 (d) 40 Correct: b 112. The only integral root of the equation

(a) y = 3 (b) y = 2 (c) y = 1 (d) None of these Correct: c 113. A man repays a loan of ₹ 3250 by paying ₹ 20 in the �rst month and then increases the payment by 15 every month. How long willit take him to clear the loan? (a) 20 months (b) 25 months (c) 30 months (d) 35 months Correct: a 114. If the two positive numbers whose difference is 12 and whose AM exceeds the GM by 2, then the numbers are (a) 18,6 (b) 16,4 (c) 14,2 (d) None of these Correct: b 115. The coef�cients of three consecutive terms in the expansion of are in the ratio 1:7:42 then the value of n is (a) 55 (b) 54 (c) 56 (d) 66 Correct: a 116. The number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words arewritten as in a dictionary, then the 50th word 124. If X follows a binomial distribution with will be

y2 + 2xy + 50|x| = 625

x2 + y2 − 2x − 4y − 20 = 0

(x − 9)2 + (y − 8)2 = 52

(x − 5)2 + (y − 5)2 = 52

(x − 0)2 + (y − 0)2 = 52

∣∣ ∣∣

2 − y 2 3

2 5 − y 6

3 4 10 − y

∣∣ ∣∣

(1 + x)n

Admission aglasem

(a) NAAGI (b) NAAIG (C) NAIAG (d) NAIGA Correct: b 117. Let be in AP. If

then K is equal to (a) 1 (b) 2 (c) 3 (d) 5 Correct: b 118. If both roots of the equation are positive, where a is a real number, then (a) (b) (c) (d) Correct: d 119. The length 'x' of a rectangle is decreasing at the rate of 6 cm/min and the width y is increasing at the rate of 4 cm/min. When x=8cm and y=4 cm, the rate of change of the area of the rectangle is (a) 8 (b) 16 (c) 24 (d) 32 Correct: a

120. If p and q are the order and degree of the differential equation

(a) p < 9 (b) p = 9 (c) p > 9 (d) None of these Correct: a 121. The solution of the differential equation

(a) (b) (c) (d) Correct: b 122. Let g(x) be the inverse of an invertible function f(x) which is differentiable at x = c, then g'(f(c)) equals (a) (b)

(c) f(c) (d)

Correct: b 123. A �ve-digit number divisible by 3 is to be formed using the numbers 0, 1, 3, 4 and 5 without repetition. The total number of waysthis can be done is

a1, a2, a3, … . . an+ + … +1

a1an

1a2an−1

1ana1

= [ + + … + ]Ka1+an

1a1

1a2

1an

x2 − 2(a − 1)x + (2a + 1) = 0

a ∈ (4, ∞)

a ∈ (−∞, 0] ∪ [4, ∞]

a ∈ (1, ∞)

a ∈ [4, ∞)

y + x3( )2

+ xy = cosxdy

dx

d2y

dx2

= ,dy

dx

2xy−y2

2xy−x2

xy(x + y) = C

xy(x − y) = C

x2y(x − y) = C

x3y(x − y) = C

f ′(C)1

f ′(c)

1f(c)

Admission aglasem

(a) 216 (b) 600 (c) 240 (d) 3125 Correct: a 124. If X follows a binomial distribution with parameters n = 100, p = ⅓, then P(X=r) is maximum, when r is equal to (a) 32 (b) 34 (c) 33 (d) 31 Correct: c 125. y = acos(log x) + bsin(log x) is a solution of the differential equation

(a)

(b)

(c)

(d)

Correct: a 126. The shortest distance between the lines is (a)

(b)

(c)

(d)

Correct: c 127. The solution set of the in equality

is

(a)

(b) )

(c)

(d)

Correct: c 128. The minimum value of 9ˣ + 9¹⁻ˣ, x ∊ R is (a) 2 (b) 3 (c) 6 (d) 9 Correct: c 129. Area of one loop formed by is (a) 0 (b) 2 (c) 4 (d) 2π Correct: c 130. The function is a solution of the DE, where are real numbers

(a)

x2 + x + y = 0d2y

dx2

dy

dx

x + + y = 0d2y

dx2

dy

dx

+ + y = 0d2y

dx2

dy

dx

x + x2 + y = 0d2y

dx2

dy

dx

→r = (4 i − j) + λ( i + 2j − 3k) and →r = ( i − j + 2k) +μ(2 i + 4j − 5k)2

√5256

√51

√5

logtan(x/3)(x2 − 3x + 2) ≥ 2

( , 2)12

[ , 2]12

[ , 1) ∪ (2, ]12

52

( , )12

52

|y| = | sinx|

y = c1 cosx + c2 sinx

c1 and c2

= yd2y

dx2

Admission aglasem

(b)

(c)

(d)

Correct: b 131. If where [.] denotes the greatest integer function, then the value of l is

(a) 0 (b) In3 (c) (d) Correct: b

132. equals

(a)

(b)

(c)

(d) Correct: d

133. is equal to

(a) (b) (c) (d) Correct: b 134. The integral dx equals (a) (b) (c) (d) Correct: c 135. The area of the region bounded by the two parabolas and y=x is (a) 1/3 (b) 2/3 (c) 1 (d) 1/6 Correct: d

136. Differentiate , 0 < x < 1 with respect to

(a)

(b)

(c)

(d)

Correct: a 137. The angle between the line and the plane 5x – 2y – 2 +17 = 0 is (a) 30° (b) 60° (c) 90° (d) 0° Correct: d

+ y = 0d2y

dx2

+ xy = 0d2y

dx2

− xy = 0d2y

dx2

∫∞

0[3e−x] dx = l

e3

3e−1

∫√3

1dx

1+x2

π

32π3π

6π

12

∫ dxsin2 x−cos2 x

sin2 x cos2 x

cotx − tanx + C

tanx + cotx + C

tanx + cscx + C

ex cosx + C

∫ ex(1 + tanx) secx

ex cotx + c

ex tanx + c

ex secx + c

ex cosx + c

y = x2

y = sin−1( )1−x2

1+x2

−2

1+x2

21−x2

11+x2

11−x2

x − 2y + z = 0 = x + 2y − 2z

Admission aglasem

138. If , then is equal to

(a)

(b)

(c)

(d)

Correct: a 139. If where [.] denotes the greatest integer function, then the value of l is (a) 1 (b) -1 (c) 0 (d) does not exist Correct: a 140. A polygon has 44 diagonals. The number of its sides are (a) 9 (b) 8 (c) 11 (d) 7 Correct: c 141. If then sin x is equal to (a) (b) (c) (d) Correct: a

142. If a, b, c are roots of the equation , then the value of is

(a) 1 (b) 2 (c) 0 (d) 3 Correct: c 143. If y = sin mx, then the value of the

determinant , where is

(a) (b) (c) (d) None of these Correct: d

144. If . Then, the value of is

(a) 1/17 (b) 1/18 (c) 1/19 (d) 1/21 Correct: c

y = ex+ex+ex+… dy

dxy

1−yx

1−yx

1−xy

1−x

limx→0 |x|| cosx| = 1

cot−1(√cosα) − tan−1(√cosα) = x

tan2(α/2)

cot2(α/2)

tanα

cot(α/2)

x3 + px + q = 0

∣∣ ∣∣

a b c

b c a

c a b

∣∣ ∣∣

∣∣ ∣∣

y y1 y2

y3 y4 y5

y6 y7 y8

∣∣ ∣∣

yn =dny

dxn

m9

m2

m3

A = [2 3

5 −2]  be such that A−1 = λA λ

Admission aglasem

145. If A = and B = and , then the value of is

(a) (b) (c) not possible (d) Both (a) and (b) Correct: c 146. Let and .Then the relation between and will be

(a) (b) (c) (d)

Correct: a 147. If , then the value of x is

(a)

(b)

(c)

(d) Correct: a 148. If R is the set of real numbers and f:R → R is a function de�ned by f(x) = sin x, then is (a) {x{ x = nt, n is an integer} (b) {xl x = 1/2 + 2nt, n is an integer} (c) R (d) null set Correct: c 149. The function f(x) =cos x is strictly decreasing on (a) (b) (c) (d) Correct: d 150. Let R be a re�exive relation on a �nite set A having n elements and let there be m ordered pairs in R, then (a) (b) (c) m = n (d) None of these Correct: a

[α 0

1 1] [

1 0

5 1] A2 = B α

α = ±1α = 4

0 < α < π, 0 < β < π cosα + cosβ − cos(α + β) = 32

α β

α = β

α > β

α < β

α =β

3

sin−1 x − cos−1 x = π

6√3

212

− 12

−√3

2

f−1([−1, 1])

ϕ

[0,π]

[0,π)

(0,π]

(0,π)

m ≥ n

m ≤ n

Admission aglasem